Choice-free topological duality for implicative lattices and Heyting algebras

We develop a common semantic framework for the interpretation both of IPC , the intuitionistic propositional calculus, and of logics weaker than IPC (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which ma...

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Bibliographic Details
Published in:Algebra universalis 2024-02, Vol.85 (1), Article 3
Main Author: Hartonas, Chrysafis
Format: Article
Language:English
Subjects:
Algebra
Duality theorem
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Topology
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Summary:We develop a common semantic framework for the interpretation both of IPC , the intuitionistic propositional calculus, and of logics weaker than IPC (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-023-00830-8